ECHAMCAL  DRAWING 

AND 

PRACTICAL    DRAFTING 


UC-NRLF 


C    2 


CHARLES  H.  SAMPSON 


MECHANICAL  DRAWING 

AND 

PRACTICAL   DRAFTING 


By 

Charles  H.  §ampson,  B.  S. 

Head  of  Technical  Department,  Huntington  School,  Boston,  Mass.  In  charge 
of  the  courses  in  Shop  Drawing,  Architectural  Drawing,  Plan  Reading,  Shop 
Sketching,  and  Machine  Design  as  conducted  by  the  University  Extension 
Department  of  the  Massachusetts  Board  of  Education. 

Author  of  "Algebra  Review,"  "Woodturning  Exercises,"  "Assignment  Man- 
ual of  Algebra,"  "Pattern  Making,"  and  various  courses  for  the  University 
Extension  Department. 


MILTON    BRADLEY    COMPANY 

SPRINGFIELD  -  MASSACHUSETTS 

1920 


B/4/a,. 


Copyright 

MILTON  BRADLEY  CO. 
1915 


PREFACE. 

Although  there  are  many  excellent  works  on  the  market  covering  in  a  more  or  less  complete  way  the  subject  of 
Mechanical  Drawing  and  Practical  Drafting,  it  has  been  my  experience  that  most  of  these  are  not  sufficiently  extensive 
and  practical  to  admit  their  use  in  schools  where  it  is  necessary  to  devote  a  large  amount  of  time  to  the  subject,  or  in 
classes  composed  of  men  wishing  instruction  of  a  practical  nature.  The  course  as  herein  presented  has  proven  its 
worth,  and  large  numbers  graduated  from  it  have  experienced  no  difficulty  in  securing  and  retaining  drafting  positions. 
Sufficient  ground  is  covered  in  the  elements  of  Mechanical  Drawing  to  insure  a  solid  foundation  for  the  work  of  a  more 
practical  nature  following. 

I  hope  that  this  book  will  prove  to  be  all  that  I  think  it  to  be.  I  am  exceedingly  anxious  to  make  any  desirable 
improvements,  and  would  therefore  welcome  suggestions  from  either  the  teacher  or  the  man  in  the  office. 

Several  important  changes  have  been  made  in  this  edition.  Material  has  been  added  which  should  improve 
the  course  presented,  and  every  effort  has  been  made  to  make  the  work  as  it  should  be.  It  is  hoped  that  these  changes 
and  additions  will  prove  valuable  to  both  the  teacher  and  student  and  add  greatly  to  the  efficiency  of  the  book  as  a 
means  of  properly  imparting  a  knowledge  of  the  subject  which  it  represents. 

This  text  is  especially  intended  for  use  in  the  class  room.  Every  effort  has  been  made  to  produce  an  ideal 
text  for  this  purpose. 

Respectfully, 

Charles  H.  Sampson. 

4360S8 


THINGS  A  GOOD   DRAFTSMAN   SHOULD   REMEMBER. 

(READ   CAREFULLY.) 

Be  neat  and  accurate,  and  keep  busy.  Study  the  problem  before  attempting  its  solution.  Don't  be  afraid  to 
ask  intelligent  questions.  Keep  the  pencil  sharp  and  the  instruments  clean.  Always  clean  a  pen  before  using.  Use 
the  T  square  by  placing  the  head  on  the  left  hand  side  of  the  board.  Use  the  triangles  against  the  T  square. 
Become  familiar  with  the  use  of  the  scale  as  soon  as  possible.  Practice  lettering  continually.  It  is  well  to  learn  to 
make  both  the  slant  and  vertical  types,  but  it  is  better  to  be  good  at  one  than  just  fair  at  either.  The  general  appear- 
ance of  a  drawing  depends  largely  upon  the  lettering.  Always  make  a  pencil  drawing  complete,  even  though  it  is  to 
be  inked  or  traced.  When  inking  or  tracing  a  drawing,  draw  the  lines  in  the  following  order:  Center  lines  (very 
light,  dot  and  dash);  all  arcs  and  curves;  full  straight  lines;  dotted  straight  lines;  cross  section  lines  (45  degrees 
when  possible);  arrowheads;  dimensions;  lettering;  border  line  and  title.  Make  dotted  and  center  lines  lighter 
than  the  others.  The  drawing  should  always  be  checked  before  being  inked  or  traced.  The  title  should  include  the 
name  of  the  object  drawn,  the  scale  used,  by  whom  drawn,  the  date  finished,  and  the  number  of  the  drawing.  Learn 
to  make  sketches  from  actual  machine  parts,  and  remember  that  a  sketch  isn't  worth  much  unless  it  is  properly  dimen- 
sioned. Before  starting  to  trace  a  drawing  it  is  well  to  rub  the  cloth  well  with  "ponce"  or  powdered  chalk.  When 
erasing  use  a  pencil  eraser,  especially  if  the  surface  is  to  be  inked  over  again.  Erase  light'y.  Make  shade  lines  by 
drawing  several  lighter  ones.  Dimensions  under  two  feet  are  usually  expressed  in  inches;  those  over  two  feet  in  feet 
and  inches.  Make  the  sheet  balance.  Draw  to  as  large  a  scale  as  possible. 


INSTRUCTIONS      (REAP  CAREFULLY) 

ALL    SHEETS  TO  BE    14i'  *  2O*"  OUT3IPE  PIME NSIONS  UNLESS  OTHER- 
WISE   SPECIFIED.    ALL  MARGINS  TO  BE  J'WIPE.  UNLESS  CALLED  FOR  DIFFERENTLY.  ALL 
TITLE5    ARE  TO  5E   PLACED  IN  THE  LOWER  RK3HT  HAND  CORNE:^  ANP  ARRANQEP 
AS  BELOW.    Po  NOT  INK  OR  TRACE  A  PRAW1N<5   UNLE55  IN^TRUCT1ON5  CALL 
TOR    SUCH  WORK.  Do  NOT  PLACE   THE  PATE   UPON  THE  PRAWINS  UNTIL  IT  15 
FINISHED.  Do  NOT  INK  INSTRUCTIONS  ON  ANY  SHEETS.  FOLLOW  DIMENSIONS .  NEVER 
5CAL.E  A  PRAWIN<5    WHEN  IMKIN^  LETTERS  HAKE  ALL  STROKES  POWN  (O)  OR  TO 

THE  reHTg.  MAKE  ARROW  HEAPS  LIKE  THIS^-  NOT  LIKE  THIS).  foRM.ALL 

LETTERS  ANP  FIGURES  50  TWAT  EACH  WOULD  FILL  A  PARALLELOGRAM  IF  Pi?OPE(?IY 
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THE   LETTERING   PLATES. 

Only  two  lettering  plates  are  required.  Both  of  these  have  been  selected  because  the  letters  represented  are  the 
types  in  most  common  use.  The  first  plate  shows  the  vertical  and  slant  styles  of  letter  generally  used  by  the  draftsman 
on  detail  drawings;  the  second  plate  represents  a  type  much  used  for  titles. 

There  are,  of  course,  very  many  forms  and  kinds  of  letters.  It  has  been  thought  best  in  this  course  to 
require  only  those  covered  by  the  first  two  plates,  hoping  that  by  so  doing  at  least  a  reasonable  degree  of 
perfection  may  be  attained  in  these  most  generally  used  types. 

One  may  obtain  many  excellent  books  on  lettering  if  occasion  demands  some  particular  style. 

The  student  will  make  use  of  the  board,  T  square,  triangles, scale,  pencil,  and  eraser  during  the  progress 
of  Plates  1  and  2. 

Figure  1  shows  how  the  T  square  and  triangles  should  be  used.  Note  that  the  head  of  the  T  square  is 
against  the  left  hand  edge  of  the  board.  Also  notice  that  all  vertical  lines  and  lines  making  angles  with  the 
horizontal  are  drawn  using  the  triangle  against  the  T  square.  Vertical  lines  should  not  be  drawn  using  the 
head  of  the  T  square  on  either  the  upper  or  lower  edges  of  the  board. 

Other  instruments  employed  during  the  progress  of  the  first  two  plates,  as  well  as  all  of  the  others,  are 
the  scale  (ruler),  eraser,  and  pencil.    The  scale  is  to  be  used  for  measuring  purposes  only  and  is  not  to  be 
employed  as  a  guide  for  drawing  lines.    The  triangles  are  to  be  used  when  lines  are  to  be  drawn  as 
indicated.     Become  familiar  with  the  use  of  the  scale  as  soon  as  possible. 


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Erasing  is  more  or  less  of  an  art.  When  it  becomes  necessary  to  erase,  use 
a  pencil  eraser.  The  resulting  surface  will  then  be  smooth.  Cultivate  a  light  touch. 
That  is,  do  not  "bear  on"  too  heavily  when  erasing.  Every  student  should 
have  a  cleaning  eraser  for  use  in  cleaning  dirt  and  surplus  lines  from  the  drawing. 
"Art  Gum"  is  recommended. 

Great  care  should  be  observed  in  the  matter  of  keeping  the  pencil  sharp.  If  a  fine  round 
point  is  always  kept  on  the  lead  it  maybe  used  for  both  lines  and  lettering.  Some  prefer  a  chisel 
point  for  use  when  lines  are  to  be  drawn.  It  is  suggested  that  the  pencil  be  sharpened  at  both  ends. 
A  point  is  then  available  for  all  purposes  because  one  may  be  made  a  chisel  point. 


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GEOMETRICAL    PROBLEMS 

All  geometrical  problem  plates  are  of  the  standard  size  (141"  x  201").  The  space  inside  of  the  f"  margin  on  plates 
3,  4,  5,  6,  7,  8,  and  9  is  to  be  divided  into  six  equal  parts.  Five  of  these  parts  are  to  be  used  for  problems.  The  sixth 
space,  in  the  lower  right  hand  corner,  is  reserved  for  the  title,  name,  date,  etc.  Great  care  should  be  observed  in  the 
solution  of  these  construction  problems.  Fine  lines  are  necessary  for  clean,  accurate  work.  The  instructor  may  well  add 
to  those  given,  especially  if  the  students  are  taking  a  course  in  Plane  Geometry.  These  problems  are  to  be  done  in  pencil. 

GEOMETRICAL   DEFINITIONS. 

A  straight  line  is  a  line  such  that  if  any  part  be  placed  upon  any  other  part  the  parts  will  exactly  coincide. 
A  perpendicular  bisector  of  a  line  is  a  line  perpendicular  to  it  and  dividing  it  into  two  equal  parts. 
A  curve  is  a  line  no  portion  of  which  is  straight. 

An  angle  of  ninety  degrees  is  formed  by  one  line  perpendicular  to  another. 

An  angle  is  the  amount  of  opening  between  two  lines  intersecting  in  a  common  point.    Angles  are  measured  in  degrees.    A  protractor  is  used  for  this  purpose. 
A  circle  is  a  plane  bounded  by  a  line,  called  a  circumference,  all  points  of  which  are  equally  distant  from  the  center  of  the  circle. 
Two  lines  are  said  to  be  parallel  to  each  other  when  they  will  not  meet,  no  matter  how  far  they  may  be  produced. 
The  mean  proportional  between  two  quantities  is  equal  to  the  square  root  of  their  product. 
A  square  is  a  plane  surface  bounded  by  four  equal,  straight  lines,  all  the  angles  being  right  angles. 
A  triangle  is  a  plane  surface  bounded  by  three  straight  lines. 

A  hexagon  is  a  plane  surface  bounded  by  six  straight  lines.  In  a  regular  hexagon  all  of  these  lines  are  equal.  A  regular  hexagon  can  be  divided  into  six 
equilateral  (all  sides  equal)  triangles. 

A  pentagon  is  a  plane  surface  bounded  by  five  straight  lines. 

An  octagon  is  a  plane  surface  bounded  by  eight  straight  lines. 

A  circle  is  inscribed  in  a  triangle  when  the  sides  of  the  triangle  are  tangent  to  the  circle. 

A  circle  is  circumscribed  about  a  triangle  when  the  sides  of  the  triangle  are  chords  of  the  circle. 

A  line  is  tangent  to  a  circle  when  it  has  only  one  point  in  common  with  the  circumference. 

A  right  triangle  is  a  triangle  containing  a  right  angle.     The  two  perpendicular  sides  are  called  legs;  the  other  side,  the  hypotenuse. 

A  rectangle  is  a  four-sided,  plane  figure,  all  of  whose  angles  are  right  angles.    The  adjacent  sides  are  of  unequal  lengths  except  in  the  square. 

The  diagonal  of  a  square,  or  other  four-sided  figure,  is  a  line  joining  two  opposite  corners. 

A  rhombus  is  a  four-sided,  plane  figure,  all  of  whose  sides  are  equal  and  whose  angles  are  not  right  angles. 

A  trapezoid  is  a  four-sided,  plane  figure,  two  of  whose  sides  are  parallel.    The  other  two  sides  are  not  parallel. 

(The  above  constitute  a  very  small  part  of  the  total  number  of  geometrical  definitions.  They  are  given  because  of 
their  relation  to  the  following  geometrical  problems.) 

10 


F.«.a 


F'1-1- 


There  are  many  other  drawing  instruments  to  be  used  by  the  student  after  the  completion 
of  Plate  2.  These  are  described  below. 

Fig.  1  is  a  representation  of  a  pair  of  bow  dividers.  It  is  used  for  spacing  off  equal  divisions  on  a  line.  It  can  be  set  to  a 
certain  dimension  and  as  many  multiples  of  that  dimension,  as  desired,  taken. 

Fig.  2,  called  the  bow  ink  compass,  is  used  for  the  purpose  of  drawing  small  circles  in  ink. 

Fig.  3  shows  the  bow  pencil  compass.    This  is  used  for  drawing  small  circles  in  pencil. 

When  a  straight  line  or  a  curve,  not  a  circle,  is  to  be  drawn  in  ink,  the  instrument  illustrated  by  Fig.  4  is  used.  This  is  called 
a  drawing  or  ruling  pen.  Ink  is  dropped  between  the  nibs  from  the  quill  which  comes  in  the  drawing  ink  bottle.  To  use  it,  set  the 
thumb  screw  in  such  a  position  as  will  give  the  desired  width  of  line  and  draw  to  the  right  for  horizontal  lines;  upward  for  vertical 
lines,  if  line  is  at  left,  and  down  if  at  right  side  of  paper.  (See  illustration  on  page  6.)  Always  keep  the  thumb  screw  outward  and 
slope  the  pen  toward  the  body. 

When  it  is  necessary  to  draw  large  circles  in  either  ink  or  pencil,  the  instruments  shown  by  Fig.  5,  Fig.  6, 
Fig.  7,  and  Fig.  8  are  used.    The  section  (Fig.  6)  is  inserted  at  A  when  pencil  arcs  are  to  be  drawn;  the  section 
(Fig.  7)  when  ink  arcs  are  desired.    The  extension  bar  (Fig.  5)  is  inserted  between  either  of  the  sections  (Fig.  6 
and  Fig.  7)  and  the  main  part  of  the  instrument  if  one  wishes  to  draw  unusually  large  arcs  or  circles.    The  legs 
of  the  compass  should  always  be  bent  so  that  the  axis  of  the  lead  or  pen  is  perpendicular  to  the 
paper. 

Fig.  9  shows  a  longer  pair  of  dividers  than  illustrated  by  Fig.  1.  This  instrument  is  used  for 
the  same  purpose  as  the  bow  divider  and  also  for  transferring  dimensions  from  one  drawing  to 
another. 

It  is  quite  necessary,  if  good  work  is  to  be  accomplished,  that  the  pencil  point  be  always 
sharp.  The  sandpaper  pad  (Fig.  10)  is  used  for  this  purpose. 

The  irregular  or  French  curve  is  used  for  drawing  a  continuous  curve,  not  the  arc  of  a  circle. 
There  are  many  different  types  of  these.  A  common  one  is  illustrated  by  Fig.  11.  The  important  thing  to 
remember  in  the  use  of  this  article  is  that  no  attempt  should  be  made  to  draw  too  much  of  the  curve  at  one 
time.  Set  the  curve  to  correspond  with  as  many  points  as  possible  and  then  draw  only  a  short  distance.  Shift 
the  curve  ahead  and  draw  another  short  distance. 
Fig.  12  shows  one  form  of  erasing  shield.  This  is  used  to  protect  nearby  lines  when  a  place  is  to  be  erased  upon. 

Just  a  word  regarding  paper,  ink,  and  thumb  tacks.  Use  no  cheap  paper  or 
ink.  "Strathmore"  detail  paper  is  excellent  for  pencil  work;  "Whatman's"  hot- 
pressed  for  ink  work.  No  ink  is  better  than  "Higgins."  Thumb  tacks  are  of 
many  sizes  and  shapes.  The  ones  with  a  beveled  edge  are  preferable  because 
the  T  square  will  slide  over  them  easily. 


r,,s 


11 


INSTRUCTIONS. 

Problem  1  — Draw  any  line  A  B.  Using  A  and  B  as  centers  and  taking  a  radius  greater  than  one  half  of  A  B, 
swing  arcs  intersecting  at  1  and  2.  Draw  the  bisector  through  1  and  2. 

Problem  2  —  Draw  any  arc  A  B.  Connect  ends  of  the  arc  by  the  chord  A  B.  Bisect  the  chord,  using  method 
of  Problem  1.  The  bisector  of  the  chord  bisects  the  arc. 

Problem  3  —  Draw  any  angle  ABC.  Taking  B  as  a  center,  draw  any  arc  1-2.  Taking  1  and  2  as  centers  and 
a  radius  greater  than  one  half  of  the  distance  1-2,  swing  arcs  intersecting  at  3.  Draw  the  bisector  through  B  and  3. 

Problem  4  —  Construct  a  right  angle  by  drawing  AB  and  BC  perpendicular  to  each  other.  Using  B  as  a 
center,  swing  any  arc  1-2,  Using  the  same  radius  and  taking  1  and  2  as  centers,  describe  arcs  B-3  and  B-4  respec- 
tively. Draw  the  trisectors  B-4  and  B-3. 

Problem  5 — Draw  any  line  AB  and  another  line  AC,  making  any  angle  with  it.  Assume  that  AB  is  to  be 
divided  into  six  equal  parts,  and  lay  off  on  AC  six  equal  divisions  of  any  convenient  size.  Draw  6-B  and  through 
the  points  5,  4,  3,  2,  and  1  on  A  C  draw  lines  parallel  to  6-B.  These  lines  will  divide  A  B  into  six  equal  parts. 

(Draw  the  lines  parallel  to  each  other  by  using  the  triangles — one  against  the  other.) 


12 


'  t 


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"2 
PROBLEM  < 

To  BISECT  A  STRAIGHT  LINE 


PROBLEM   2. 
Tb  BI5EX1T  AN  ARC  OF  A  CIRCLE 


PROBLEM  3 
Tb    BISECT    AN    ANGLE. 


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Tb  TRI5ECT   A   RIGHT  AN<5LE    ABC 


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PROBLEM  5 
TO  DIVIPE  A  LINE  INTO  ANY  NUMBER  OF 


GEOMETRICAL    PROBLEM 5 

PRAWN    3Y 
DATE 

PLATE    NO.    3 


INSTRUCTIONS. 

Problem  6 — Draw  any  line  C  D  and  divide  it  into  any  number  of  unequal  parts.  Draw  any  other  line,  as 
A  B,  of  a  different  length  than  C  D.  Draw  A-4,  making  any  angle  with  A  B,  and  on  it  lay  off  the  same  distances  as 
given  on  C  D.  Connect  4  with  B,  and  through  points  3,  2,  and  1  draw  lines  parallel  to  B-4.  These  lines  will  divide 
A  B  into  the  same  proportional  parts  as  C  D. 

Problem  7 — Draw  any  circle.  Draw  any  diameter,  as  1-5.  Using  1  and  5  as  centers,  describe  arcs  passing 
through  the  center  of  the  circle.  The  distances  1-3,  3-6,  6-5,  5-7,  7-4,  and  4-1  are  equal. 

Problem  8 —  Draw  any  line  B  C,  and  take  any  point  A  above  it.  Using  A  as  a  center,  describe  an  arc  cutting 
BC  in  two  points,  as  1  and  2.  Taking  1  and  2  as  centers  and  using  a  radius  greater  than  half  of  1-2,  swing  arcs  inter- 
secting at  3  and  4.  Draw  the  perpendicular  through  3  and  4. 

Problem  9  —  Draw  any  line  A  B.  Using  A  as  a  center,  swing  any  arc.  With  same  radius  swing  arcs  from  1 
and  2  as  centers.  Using  2  and  3  as  centers,  swing  arcs  intersecting  at  4.  Draw  the  perpendicular  A-4. 

Problem  10 — Draw  A  B,  and  at  any  points  1  and  2  erect  perpendiculars,  using  the  method  of  Problem  9. 
Set  the  compasses  to  a  radius  E  F  and  swing  arcs  cutting  the  perpendiculars  at  3  and  4,  using  1  and  2  respectively 
as  centers.  Draw  C  D  through  3  and  4. 


14 


4- 

A 

A  \\ 
/  s  \\ 

/  \         \    \  \ 

/  ^         \  ,  -  ^  p 

AT-, 

/ 

\ 

B    J 

\ 

^ 

2 

V-  —  ^ 

PROBLEM  7 
To  PIVIPE  A  CIRCLE  INTO  six  EQUAL  PARTS 

X--...--'/ 
X^ 

PROBLEM  8 
TROM  A  POINT  A  ABOVE  THE  LINE  PC  TO 

DRAW   A   PERPENDICULAR.   TO   BC. 

*       <*           i                        i         i      n 

C       I               i     3   p 
PROBLEM  6 

To  WIPE  A  LINE  AD  INTO  W1E  PROPORTIONAL  FfcRTS 
AS    CC>. 

x£- 

/\ 

4'  "~"^N 

\ 

'!              r 

GEOMETRICAL  P!?OeLEM5 

PRAWN    BY 
PATTE 
PLATE    NO  ^« 

T    T 

>|C                        ^ 

^-!-x.x              ,x-TH 
!      \ 

n       \           ,'        12     e 

A                    < 
PROBLEM  9 

ON   A  GIVEN    LINE   AB  TO   ERECT    A. 
PTRPENPICULAR    AT  A 

A 

PROBLEM  lo 

To    PRAW    CP  P/\RAU(_eU   TO    AB  AT  Av 
PI5TANCE     EF  ABOVE    IT. 

INSTRUCTIONS. 

Problem  11 --Draw  any  line  AB  and  take  any  point  C  above  it.  From  any  point  1  on  A  B  swing  an  arc 
through  C.  Using  C  as  a  center,  and  the  same  radius,  describe  arc  1-3.  On  1-3  take  a  distance  equal  to  2-C.  Draw 
D  E  through  C  and  3. 

Problem  12 — Draw  any  angle  BAG.  Using  A  as  a  center,  describe  an  arc  as  1-2.  Draw  a  line  D  F,  and 
taking  D  as  a  center  draw  an  arc  having  same  radius  as  1-2.  On  arc  3-4  take  a  distance  equal  to  1-2.  Draw  D  E. 

Problem  13 — Draw  any  two  lines  AB  and  CD,  and  take  any  point  F  between  them.  Using  F  as  a  vertex 
draw  any  triangle  F-2-1.  Take  point  4  anywhere  on  CD,  and  draw  4-E  and  4-3  parallel  to  2-F  and  2-1  respective!,. 
Draw  3-E  parallel  to  1-F.  Draw  the  line  through  E  and  F. 

Problem  14  —  Draw  any  two  lines  AB  and  CD.  Draw  another  line  EF  whose  length  is  greater  than  AB 
plus  C  D,  and  on  it  take  1-2  equal  to  A  B  and  2-3  equal  to  C  D.  Bisect  1-3,  using  the  method  of  Problem  1.  Taking 
4  as  a  center,  describe  the  semi-circumference.  At  2  erect  a  perpendicular  to  E  F.  2-5  will  be  the  mean  proportional 
between  1-2  and  2-3.  (The  mean  proportional  between  two  quantities  is  equal  to  the  square  root  of  their  product.) 

Problem  15  —  Take  any  line  A  B.  At  B  erect  a  perpendicular,  using  method  of  Problem  9.  Using  B  as  a 
center,  draw  arc  A-1.  Using  A  and  1  as  centers,  draw  arcs  B-2  and  B-3-2  respectively,  thus  determining  the  remain- 
ing corner  of  the  square. 


16 


c^ 

^^\ 

*^C° 

\                                 I         N 

\        /    \ 

r?^^— 
" 

\ 

p 

^--^^^N          \  N\ 

3  ^, 

\ 

3*^ 

C'^**'                  I  V\E__—  —  «-  f""""" 

\  /      \ 

^^\ 

«\/          '•''' 

A                      '  <"-                           2                  & 

A 

1' 

C 

A                                   f                 » 

PROBLEM  H 

PROBLEM  12 

PfJOBLEM   )"5 

THROUGH  A  POINT  C  TO  PRAW  A  LINE 

16    CONSTRUCT    AN   ANGLE    EQ.UAL  TO  A 

THROUGH  A  GIVEN  POINT  F"TO  PRAWAUNE 

PARALLEL.   TO   AD. 

GIVEN    ANOL.E     ABC 

V»HICH  WOUL.P  MEET  INTERSECTION  OF  AP 

AMP  CD.  PROPOCEP. 

/                                          X 

* 

1 

c 

• 

\/              \  •> 

A     n                     \ 

M                          *           a         U 

/    ^     S\ 

"-•iN 

<5EOMtrTI?lCAL  PROBLEMS 

• 

A             C                      17 

^^  / 

PRAWN  BY 

\' 

J 

PROBLEM  15 

ON  A  GIVEN   LINE     AS  TO  CONSTRUCT  A   SQUARE 

PATE 
PLATE    NO.  5 

PROBLEM    14-. 

Tb  FINP    THE     MEAN    PROPORTIONAL. 

BETWEEN      AB    ANP   CP. 

17 


INSTRUCTIONS. 

Problem  16  — Take  any  line  A  B.  With  A  and  B  as  centers,  and  a  radius  equal  to  A  B,  swing  arcs  intersecting 
at  1.  Draw  A-1  and  B-1. 

Problem  17 —  Draw  any  three  lines  A  B,  CD,  and  E  F.  Taking  A  as  a  center,  and  a  radius  equal  to  E  F,  swing 
arc  G  H.  Taking  B  as  a  center,  and  a  radius  equal  to  C  D,  describe  arc  L  M.  Complete  the  triangle. 

Problem  18 —  Draw  any  line  A  B.  Using  A  and  B  as  centers,  and  a  radius  equal  to  A  B,  swing  arcs  intersecting 
at  O.  Using  O  as  a  center,  and  the  same  radius,  draw  the  circle.  A-5,  5-4,  4-3,  3-2,  and  2-B  are  each  equal  to  the 
radius  of  the  circle. 

Problem  19  —  Draw  a  square,  as  A  B  C  D,  and  draw  the  diagonals  AC  and  B  D.  Using  A,  B,  C,  and  Das 
centers,  describe  arcs  passing  through  1.  Connect  points  where  the  arcs  cut  the  sides  of  the  square  to  obtain  the 
octagon. 

Problem  20 — Draw  a  line  A  B.  Using  A  and  B  as  centers,  and  A  B  as  a  radius,  swing  arcs  intersecting  at 
2  and  9.  Draw  M  N.  Using  9  as  a  center,  describe  an  arc  through  A  and  B,  cutting  the  first  arcs  drawn  at  3  and  5. 
Draw  3-4-6  and  5-4-7.  Draw  A-7  and  B-6.  Taking  7  and  6  as  centers,  and  a  radius  equal  to  A  B,  swing  arcs  inter- 
secting at  8.  Complete  the  pentagon. 


18 


PROBLEM  16 

ON  A  GIVEN    LINE   TO  CONSTRUCT    AN  EQUILATERAL. 
TRIANGLE. 


A    C- 


PROBLEM  17 

THREE  SIPR  OF  A  TRIANGLE.  TO 
CONSTRUCT  THE  FIGURE.. 


PROBLEM  18 

ON   A  LINE   A&  TO   CONSTRUCT  A  REGULAR 


5^-Ov\        I''',-'- 

x 

^-?!     ^:~~- 


•  B 


PROBLEM  19 
WITHIN  A  SQUARE.  TO  CONSTRUCT  AN  OCTAGON 


PROBLEM   2O 
ON  A  GIVEN  LINE  A&  TO  CONSTRUCT  A  PENTAGON 


PROBLEM? 


PRAWN    PY 


PLATE    NO 


19 


INSTRUCTIONS. 

Problem  21  --Draw  any  line  A  B,  and  at  A  and  B  erect  perpendiculars,  using  method  of  Problem  9.  Bisect 
the  right  angles  formed  by  the  perpendiculars  and  A  B  produced.  A-1  and  B-2  will  be  sides  of  the  octagon.  Draw 
1-2  and  take  3-5  and  4-6  equal  to  A  B.  Take  5-9  and  6-10  equal  to  A-3  or  B-4.  Draw  a  line  through  5  and  6  and  take 
5-7  and  6-8  equal  to  1-3  or  2-4. 

Problem  22 — Draw  any  triangle.  Bisect  any  two  angles,  using  method  of  Problem  3.  The  intersection  of 
the  bisectors  is  the  center  of  the  inscribed  circle. 

Problem  23  —  Draw  any  triangle,  and  bisect  any  two  sides,  using  method  of  Problem  1.  The  intersection  of 
the  bisectors  is  the  center  of  the  circumscribed  circle. 

Problem  24 — Draw  a  circle,  and  take  any  point  A  on  the  circumference.  Draw  a  radius  produced  through 
A,  as  O  P,  and  on  it  from  A  lay  off  equal  distances  A-2  and  A-3.  Using  2  and  3  as  centers,  erect  a  perpendicular  at  A. 
This  will  be  the  required  tangent. 

Problem  25 — Draw  any  arc  of  a  circle.  Take  any  point  A  on  the  arc  and  draw  any  chord  A-1.  Bisect  A-1 
and  draw  the  bisector.  Taking  A  as  a  center,  swing  an  arc  through  3  and  lay  off  3-4  equal  to  3-5.  Draw  the  tan- 
gent through  4  from  A. 


10 


.. _T 
5          6 


SI;-  '""^'  I  ^JX 

,*r-37  -\-pr-A, 


PROBLEM  21 

ON  A  GIVEN  LINE  AB  TO  CONSTRUCT  AN 
OCTA<SON. 


PROBLEM  22 

WITHIN  ft  TRIAN-3LE  TO  INSCRIBE.  A  CIRCLE 


PROBLEM 
TO  CIRCUMSCRIBE  A  CIRCLE  ABOUT  A 
TRIANGLE., 


24- 


To  PRAW  A  TAN<5ENT  TO  A  CIRCLE  AT 
A    <5tV£N    POINT    A  . 


PROBLEM 
To  PRAW  A  TANGENT   TO  A  CIRCLE  AT  A 

9IVEN  POINT  A  WHEN    CENTER  IS  INACCESSIBLE 


PROBLEMS 

DRAWN    BY 
PATE 

PLATE    NO     *7 


21 


PROBLEM  26 
CONSTRUCT    AN  AN<SLE   OF    15  PE<5REE5 


GIVEN    AN  ANGLE.    AMP  THE  \NCLUPEP 

SIPE-5    OF    A  TKIAN<SLE    TQ   CONSTRUCT 
THE 


PROBLEM  28 

<3lveN      TWO   ANGLES   ANIP  ONE    SIPe  Of= 
A  TRIANGLE    TO   CONSTRUCT  THE   TRIANGLE 


ONE   LE<3 
A  RIGHT  ANGLE 

THE  TRIANGLE- 


THE  HYPOTENUSE  OF 
TRIANGLE.  TO  CONSTRUCT 


THE  APJACENT  51PE5   OF  A 
TO    CONSTRUCT   THE 


GEOMETRICAL    PROBLEM  5 


C7PJAWN      BY 


.     8 


22 


PROBLEM  31 

""16    CONSTRUCT     A    'SQUARE    HAVING 
GIVEN    THE    PIAC5ONA.U 


PROBLEM 

Tb    CONSTRUCT    A   RHOMBUS     HAVING- 
GIVEN  A  SIPE   AMP    THE   ACUTE 


PROBLEM 

To    CONSTRUCT    A  TRAPEZOIC?    HAVING 
GIVEN    THE.    FOUR    SIPES. 


PROBLEM 

ANY  THREE   POINTS.   PRA\s/ /S 
CIRCLE  WHICH  5HALL  PA55  THROUGH 
THESE    POINTS 


PROBLEM 

AN  OCTAC.ON  USING  THE  4-5° 
TR/A.NGLE.  ANC?  1N5C,(?IBE  A  CIRCUE. 
IN  IT  ANP  CIRCUMSCRIBE  A  CIRCLE. 

ABOUT    IT. 


GEOMETRICAL 

PRAWN     BY 


PROBLEMS 


PLATE.  NO.   Q 


23 


CONIC  SECTION   CURVES. 

There  are  several  conic  section  curves  used  to  a  considerable  extent  by  draftsmen.  Some  of  the  methods 
used  for  the  construction  of  these  curves  are  illustrated  by  the  figures  on  Plates  10  and  11.  There  are  many  methods 
in  use  for  the  construction  of  these  curves,  but  the  ones  given  are  among  the  most  simple  of  those  generally  employed. 

If  a  regular  cone  was  cut  by  a  plane  parallel  to  the  base,  the  outline  of  the  cross  section  would  be  a  circle.  If 
the  cutting  plane  was  not  parallel  to  the  base  and  did  not  cut  the  base,  the  outline  of  the  section  would  be  an  ellipse. 
If  the  cutting  plane  did  cut  the  base,  the  outline  of  the  curve  of  the  section  would  be  a  parabola.  If  two  planes  were 
passed  through  a  cone  parallel  to  the  altitude,  and  at  an  equal  distance  each  side  of  it,  the  curves  of  the  hyperbola 
would  be  obtained. 

An  ellipse  is  a  curve  which  is  the  locus  of  a  point  moving  in  a  plane  so  that  the  sum  of  its  distances  from  two 
fixed  points  in  the  plane  is  constant. 

A  parabola  is  a  curve  -which  is  the  locus  of  a  point  moving  in  a  plane  so  that  its  distance  from  a  fixed  point  in 
the  plane  is  always  equal  to  its  distance  from  a  fixed  line  in  the  plane. 

An  hyperbola  is  a  curve  which  is  the  locus  of  a  point  moving  in  a  plane  so  that  the  difference  of  its  distances 
from  two  fixed  points  in  the  plane  is  constant. 

The  drawing  of  these  curves  is  required  so  that  the  student  may  acquire  proficiency  in  the  use  of  the  irregular  curve. 
The  intention  is  not  to  emphasize  the  mathematical  importance  or  connection  with  the  cone. 


24 


,       ones  AB  /p"  /asty  asx/  fife  m/nor-  axes  C£>    7'fay.    Tfte  e////>se  of  r/y.  f  u  draw)  £>y 

of  ffa/77/fl&!}.    ~%?te  a  strip  of  popfr  and ' an/ts  fdye  /ay  o/f  ff=*£  nwor aw  or  5"  and A/-£  snmor  ax/i  or 3£~  A&ep  Are  fv/af 
off  #?e  m//?or  ax/s  0/?af  #K  /w/7/  Z?  a/ways  os?  f he  major.  S/x>f'ft?ffo//7fc3  ofr/n/netf  £y  fFvo/v/ha  tfie  Sre. 
the  fnn??</Jar  cc/nv.  7fl  ffy  2  tote  Of/  ona  OF  egt/a/  fo  d/fSf r&Ke  fiefaeen  majorarxf  mfor  axes , 
OS-  f<z&0/  fa  Tfi/ve1  four/frj  <?/  &//  or  Of.        _  6t>/0?  e  .f^e  asid '//  at  centers  afraw  ." 

TA 

Place  no  dimensions  on 
finished  sheet 


Difference 

major  and  minor  U 


ELLIPSES 

5CALC    FULL  SIZE 
BY 


RLATE    NO   fO 


25 


recfang/es  of  d/mffns/bns   as  q/ven    f/s/na  fbe  <//v*sferi  cfrv/d?  rfbf  s/Jes  a/  /fa  /vcfa/y/fs 
CO  cofframs  fo/S  as  ma/yy  e/''v'f/os?s  as£>£.  <f/?af  f/?af~  //r  f/y.2  GJ~  coa-faim  fta/f  as  /n0s 

as  (r/f.    Pravs  /Ae  //hes  and  cofmec/~ p<v/?&  jAow/?  w/na  fAe  /rreyu/ar-  curve.     The  cc/ryr  a/  fhefirjf-  f/yvrf  a 
ffle  para6o/a ;  #>af  o/  Me  second  -/-haf  a/  #x?  6y per  tote ,   /I 5  /f  caffed  Me  afocitJa  or>J  PE  foe  doub/e 
a   ca//e<t  fAe  ox's    ancf  f^Q   //*•  c/ot/£>Af  orcft'/taff. 

Place  no  dimensions  on  the  finished  Sheet 


PARABOLA   ANP  HYPERBOLA 

SIZE. 
^"^  N0      H 


26 


DIMENSION    UNE.- ARROW  HEAP 


FVLU    LIN( 


5HAC7E    UNE. 


POTTEC?   LlNE. 


CENTER    LINE 


o       czv7Wf/7Ar/»/~  sco/f 
7*  f&f  *•*»***#.     cro,s-f*ct,on   //nes  ore    dro^n 


MALI.    IRON 


WR006HT    STEEL- 


LEATHER. 


WROUGHT      IROM 


OL-ASS 


WOOC> 

5TANI7ARI7  LINES  ANP  CR05S  SECTIONS 
PRAWN     Bf 
PATE. 

PLATE     NO     12. 


27 


\ 


toy  ay/  fyvongskt  so  ftaf  genera/ 
of  jfntJhed  jfieef  M'//  &$  Me  /rtv  sheet: 


USE   OF  TRIANGLES 

BY 
PATE 

NO.    !>- 


28 


or? 

very  ///XT  /itfes 
.  /2tPSr. 


roef/us  antf  a/>riv  center  fcj 

on      S*  />'/7f. 


SHADING 

SCALE     FULL   SIZE 

PRAWN    BY 

PATE. 

PLATE  NO 


29 


ORTHOGRAPHIC   PROJECTION. 

Orthographic  projection  is  a  process  in  drawing  by  the  use  of  which  we  find  the  projection  of  lines,  surfaces, 
or  solids  upon  three  planes,  namely,  the  horizontal,  the  vertical,  and  the  profile.  To  illustrate  how  these  planes  are 
related  to  one  another,  may  we  suppose  that  an  object  such  as  a  rectangular  pyramid  has  been  placed  upon  the  bottom 
of  a  rectangular  box.  The  top  of  the  box  represents  the  horizontal  plane,  the  rear  or  front  face  the  vertical  plane,  and 
the  right  hand  face  the  profile  plane.  Projections  of  the  object  may  be  obtained  upon  all  of  these  planes  by  drawing 


HORIZONTAL  PLANE 


HANE. 


A 


perpendiculars  from  the  several  points  of  the  object  to  the  different  planes.  The  points  at  which  the  perpendiculars 
pierce  the  planes  are  the  projections  of  the  points  of  the  object  upon  the  planes.  If  the  points  are  connected,  the 
projection  of  the  faces  will  be  obtained.  If  the  three  planes  of  projection  are  made  into  one,  the  three  views  of  the 
object  will  appear  as  we  must  represent  them.  Take  particular  notice  of  the  fact  that  lines  not  parallel  to  the  planes 
appear  shorter  in  the  projection.  In  orthographic  drawing  objects  appear  as  they  are  projected,  not  necessarily  as 
they  actually  are.  Dimension  all  plates  from  now  on  unless  otherwise  specified. 


30 


START     WITH  THIS   Y1CW   IN 
CENTER.    OF   5HEET. 


I 


-tt 


77i/j   ihtrr  ftpftttms  tfie  ft/a  and  Snypf 
of  a  cub?  sAo^ft  in  var/ous  posrf-ions.    TT>e  f/noi  afipeor&n(f 
of  //*•  f/wbecf  sherf  sfiou/a  be  Mf  above 


CUBE 


FULL  SIZ 
N  BV 
PATE. 


PLATE  NO 


15 


31 


7fe>  fop,  f/z>/?f  am/jje/e  v/ewj  of  a 

pns/r?  arp  j frown  aAavf.    /IB  and  CPare  draws? 

//?  crvy  canve/?/e/?f-  p/ace.  O  /»  used '  <yj  a 


ftere  shows?.   Tfif  J/'df  wet*/ 

r  t/rffw?  i/s//?g  f tie  m?f foot 
of  tte  preceding  prvb/em. 


TRIANGULAR  AMI?  HEXAGONAL  Pi?|SMS 

SCALE     FVL 

PRAV/N   BY 


PLATE    NO 


32 


J 


L 


in 


The  from*-  arxf  ityo  y/fws  of  a 
P/-/J/7?  off  fyrsp  s/xrw/f. 


o/  a 


fte  fo/o 


T?ECTAN<5ULAK  ANP  TRIANGULAR  PRI5M5 

SCALE    FULL  SIZE 
PRAWN    BY 


PLATE    MO 


17 


33 


Tnc  franf  and  Jiafe  v/ews 


ftp  view  qf  foe 

atwve  by  dsaMng  a  2 "  are/e,  div/d/nq  ffc  c/r  . 

j/rfo  //ye  eaua/ parti  ana  coffnfcMg  the  f>o//?fc  obfowea 

ttx?  front  and  j/cte  v/ews.       Make  the 
" 


EECTANQULAR  PYRAMIP/  PENTAGONAL  PRI5M 


5CALE    FOUU   SIZE. 
BY 
CVKTE. 


P4-ATE    NO 


.   ID 


34 


f 

s 

[ 

Tf 

i 

i 

J  ,* 

i    -IN 

1         V 

> 

1 

i 

i                i 

INSTRUCTIONS 

PRAW    ON  WHITE.  PWER    W1P  INK  .  T(?Y  TO  GET  A  NOTICEABLE 

DISTINCTION  BCTWECN  THE  pirrecENT  KINPS  OF  UNts    FOLU 

LINES    ABC   TO   BE.    Hf/NyiER    THAN    OOTTFD    AW  p(MEN5lON   LiNfS 


MACHINE     DETAIL 

5CA.LC      FULL-     SIZE 
PRAWN     BY 
PATE 


NO. 


35 


MAKE  A  PRAWINC  IN  ORTHOGRAPHIC  PROJECTION  OF  A  HEKA<5ONAL  PRISM  HAVING  AN  ALTITVPE  OF  3",  THE 
DIAMETER  OF  THE  INSCRIBED  CIRCLE  OF  THE  BASE  BEIN<3  }|".  ONE  OF  THE  NARROW  FACES  IS  TO 
REST  ON  THE  HORIZONTAL  PLANE  ,  THE  HEXAGONAL.  BASES  SEIN<S  PARALLEL.  TO  THE  PROFILE  PLANU- 


PRAW    A     5QOARE.     PYRAMIP     IN    ORTHOGRAPHIC     PROJECTION     RESTING    ON    ITS    BASE     AND 
ANGLE.    Of    15°   WITH    THE     VERTICAL.     Rl_ANE.      THE     BASE    \3     2"   3GJUA.RE.  J  THE.    ACTITUC'Er 


AM 


HEXAGONAL  F^ISM  ANP  5QUARE  PYRAMIP 


5CAL.E 


FOL.L.    SIZE- 
BY 


HO 


36 


-134 


4'i 
*i 

7  1 


•4, 
J 


-2*- 


FINI5H     OVER  ALL       WROUGHT   IRON 


INSTRUCTIONS 

DRAW  ON  WHITE    PAPER    AND  INK 


BLOCK  POR  REPLACING   LOCOMOTIVE 

SCALE     rut-L. 

B-r 


PLATE     NO 


01 

.        21 


37 


THE   USE  OF  THE  SCALE. 

(READ  THIS  CAREFULLY.) 

Up  to  this  point  all  drawings  have  been  made  full  size.  That  is,  all  dimensions  as  given  on  the  paper  are  repre- 
sented by  distances  possessing  true  value.  It  is,  of  course,  easy  for  any  one  to  see  that  it  would  not  be  possible  to 
make  all  drawings  full  size.  The  drawing  of  a  house  or  a  large  piece  of  machinery  obviously  could  not  be  made  of 
the  same  size  as  the  object  itself. 

The  scale,  used  by  draftsmen,  has  been  so  arranged  that  drawings  may  be  made  bearing  almost  every  propor- 
tion to  the  object  without  doing  any  actual  computing.  This  is  not  often  true  of  the  six  inches  equal  one  foot.  That 
scale  is  rarely  given,  but  any  one  who  can't  divide  a  quantity  by  two  and  get  the  correct  result  should  not  adopt  a 
drafting  or  technical  calling.  But  if  one  wished  to  make  a  drawing  one  quarter  size  he  would  first  divide  twelve  by 
four,  the  result  being  three,  and  on  the  scale  find  a  distance  of  three  inches  properly  divided.  An  examination  of 
this  three-inch  scale  would  show  how  it  is  possible  to  make  a  drawing  one  quarter  size  without  computation.  The 
three  inches  is  divided  into  twelve  equal  parts  just  the  same  as  the  full  scale.  Each  one  of  these  parts  represents  one 
inch  in  just  the  same  way  that  one  twelfth  of  the  full  scale  equals  one  inch.  The  inches  are  subdivided  on  the  smaller 
scales  in  the  same  way  as  on  the  full  size  if  it  is  practicable  to  do  so.  Measure  from  the  three-inch  scale  as  from 
the  full  scale  and  without  computation. 

Study  the  one  eighth  or  one  and  one  half  inches  equal  one  foot  scale,  and  in  addition  all  of  the  others  down 
to  the  one  eighth  and  one  sixteenth  inches  equal  one  foot.  Don't  forget,  of  course,  that  all  dimensions  must  be  num- 
bered full  size.  It  hardly  seems  necessary  to  give  the  reason. 


PLATE  22. 

Divide  the  sheet  inside  the  border  into  six  equal  parts  in  the  same  way  as  previously  done  for  the  Geometrical 
Problems.     In  the  six  spaces  thus  formed  draw  according  to  following  directions:— 

Space  1 — Make   three  views  of  a   rectangular  pyramid,  the  base  of  which  is  two  inches  by  two  and  one  half 
inches,  the  altitude  being  four  and  one  half  inches.     Call  this  Figure  1. 

Space  2 — Make   three   views   of   the   object  of   Figure  1    revolved    about  an  axis  perpendicular  to  the  vertical 
plane,  the  base  making  an  angle  of  thirty  degrees  with  the  horizontal  plane.     Call  this  Figure  2. 

Space  3 — Make  three  views  of  the  object  of  Figure  2   revolved  about  an  axis  perpendicular  to  the  horizontal 
plane,  the  edge  of  its  base  making  an  angle  of  fifteen  degrees  with  the  vertical  plane.     Call  this  Figure  3. 

Space  4  —  Make  three  views  of  the  object  of  Figure  1   revolved  about  an  axis  perpendicular  to  the  profile  plane, 
the  base  making  an  angle  of  ten  degrees  with  the  horizontal  plane.     Call  this  Figure  4. 

Space  5  —  Make  three  views  of  the  object  of  Figure  3  revolved  about  an  axis  perpendicular  to  the  profile  plane, 
the  base  making  an  angle  of  fifteen  degrees  with  the  horizontal  plane.    Call  this  Figure  5. 

Space  6  —  This  space  is  reserved  for  the  title.    Arrange    it   in    the   same   way   as   for  the   geometrical    plates. 
The  title  is  Orthographic  Projection.     The  scale  is  six  inches  equal  one  foot. 


39 


DEVELOPMENTS. 

(READ   CAREFULLY.) 

The  development  of  the  surfaces  of  a  solid  requires  that  all  of  the  faces  of  the  solid  shall  be  shown  upon  one 
plane,  all  of  them  being  in  their  true  size  and  all  of  them  bearing  the  same  relation  to  each  other  in  the  development 
as  in  the  solid  itself.  Great  care  should  be  observed  in  the  securing  of  the  lines.  If  these  are  not  obtained  in  their 
true  length  the  development  can  not  be  correct.  This  is  well  illustrated  in  the  case  of  the  pyramid  and  the  cone.  It 
will  be  noticed  here  that  the  edge  must  be  swung  around  into  the  vertical  plane  before  the  true  length  can  be  pro- 
cured. A  good  check  on  the  work  is  to  cut  out  the  development  and  fold  it  together.  If  the  surfaces  as  developed 
do  not  enclose  the  solid  whose  surfaces  it  is  supposed  to  represent,  there  is  a  mistake  somewhere. 

In  actual  practice  many  things  are  cut  out  from  metal,  folded  together,  and  soldered  and  formed  into  useful 
things  of  one  kind  or  another.  All  of  this  work  is  based  upon  and  is  a  practical  application  of  these  development 
problems.  When  work  of  this  sort  is  to  be  done  allowance  should  always  be  made  for  a  lap.  Otherwise  the  sur- 
faces could  not  be  soldered  together.  It  is  suggested  that  all  students  develop  some  of  the  common  receptacles 
familiar  to  them.  A  sheet  of  suggested  objects  is  given  at  the  end  of  this  chapter. 


>-«.- 


tX 


G/rm*7/?p  shows  /fie  ftp  ffn</  fr/mrf"  Y/ews  of 
a/so  itif  d<?vr/o/y/nertf:  Abfc  Mof/ftf 
o/  dhrMtny  a//  a/ ft f /sees  fyfi///s/ze  i 


PCVE  LOPMENT  Of  A  CUPE 

SCALE      FULL  SI^E- 
BY 


PLATE     NO 


.Tb 


41 


v/ewj  of  />yram/aas  s/iawn  . 

fenfth  of  edge  sir/fta  one  Cfftitif  O'as  a  cf/ffer  and 'O'C.  ff 
a  raJ/f/s.  P/viecr  //urn  C>  fi>  /I.    Od  vf/7/  A°  /A?  focf/us  ib  me 
otrfa/'n/ng 


fCVf  LOPMENT  Or  A  PYRAMU7 


o 


PRAWN   BY 
PATE 

PLATE    NO. 


42 


BI5CCT  THC  ANGLES  TO 
OBTAIN    THf  VTRTCX 


Jff}/rucr/am 


p^  ^  fa^  jyf  ajfa.frxffyy  fo  a/yfo  attain  ft*  font  v 
of  fne  pyramid  '  /a  /he  uwa/  manner  6/s/fy  O'a)  a  cm/er  d?sc/rh?orcs  cuff//y  / 
of  xy.ond  z  Prq/ect  abw  fo  get  d.  Band  C  P/zrv  QA.OB  and  OC  /Jake 


attain  ft*  font  vw 
/IN 


.  .  . 

ffv  fr/ony/e  Q  eyao/  /c  /6e  £a;e  of  ftf  py&m/c/  Tfc  /a/era/  faces 
cansfntcted  //?  fne/r  frue  size  ufvn  Me  edges  a/  Q  Thu  //  fc/fas  an  eterase 
/or  /fie  sfadenf 


DELVCLORTACNT  Or-TRlAN<aULAI? 

FULL    5IZE. 


PLATE     NO- 


43 


I    I  I 


|»  14  |»  |*   |T    |     I      |      I     |     |     |     | 


1,11 


I 


I i 


B 

r,       *  v^.  y  ^       /*/      4  ,„  ^ ^  PEVELOPMENT  OF  A 

/wi^  /%•  jnar  ana  fop  v/ei^s  of  me  cylinder  or  me  <,O\LE 

sheef.  Cbmfyvcf  ffie  cteve/opmenf  iy  draw/rq  a  rfcfang/e  rtfoji?  a/Hfad* 

fftp  some  as  fkc  otfituag  or  fae  cy/mder  anef  iv/f/a^e  /eno?/?  /J  Me  same  as  f/te 
*-  of  J-fie  arcismfervnce  of  a  6ase>  of  the  cyAMftr.     '""—  '  •"-  "•' — ' —  *"" 


ffte  c/rcu/ar  Pases. 


r^  i    R 

PKAWN    BY 


44 


f 


?/*?  frzwf <jf?d /op  v/evs  of  toe  cone  of  fte  fc/f  o/  the 
Jfreff~.    &t~a\*s  rf?f  cfeve/o/omtnt  fry  iw/na/na  on  ore  us/no  o  r&cftttj  OA .  Of? 
7/>/j  on.  /oy  o/S  Z?-f-  (//v/iw/75  foe/?  eq.ua/-fo  one  of  /A?  2-^  aivh/ons  of- 
the  c/rctffr?fereace  of  //w  base.  Pra\*/  -ftx?  c/rcufar  base  fanaent  -to  the 
an  or  any  &a¥HMt*r  pofah 


DEVELOPMENT  OF  A  CONE. 

SCALE     rOLI 

Pf^AWN    BY 


PIA7E    NO. 


45 


II    IN. 


I   234- 


I    I    I    I    !    I  |    I    I    i  |    I    I    |    I    i 

I  '  I  I  i  I  M  i  !  i  i  |  i     I 

t     I    '  i     la  I  • 

I  LJ— ^ 


Tfif  space  6-8  ffioy  6f  erf 

8         any  convenient-  • 
'  t   -..     .-vA^  j*. 


DEVELOPMENT  OF  AN  E1DOW 

run.  SIZE. 

BY 
PATE  0/2 

PLATE  No.  AD 


46 


I 


F71? 


DC YELOPMENT  Or  &  RCCIWWUUK 
PRI5M  CUT  BY  A  PLANE. 

SCALE     FULL   5RE- 
BY 


NO. 


47 


r 


PfVELOmENT  CF  RECT.  PYKAMIP  CUT  BY  PLANE, 
-ei    roui-    srzE- 

PK.A.Vv'M     BV 

TE: 

MO. 


48 


PEYELOPMPNT  OF  HEXA50NM.  PYRAMIP  CUT  BY  PLANE. 


PLATE       NO 


14- 


3       4-      sr      V*     7 


cy//nder  as 
c/ 
ne 


. 

of  /A"  /afera/  surface  as 
of  //?e  /cw<?r  terse 


/J  f/ye  same  as 


PFVFLOPMENT  Of  CYLINPER  CUT  BY  PLANE 

B-r 

& 

PL.ATE 


.32 


50 


PEVELOPMENT  OF   FOUR  PART  ELPOW 
SCALE     FULL    SIZE. 
PRAWN     BY 
CVCTE. 

NO. 


51 


Plates  34  anc/35  require  the  representation  of  the  development  ofa  cone,  after  beinq  cut  by  a  plane  in 
different  positions.     The  some  sije  cone  is  used  in  both  eases. 

P/afe  349hou/d  show  the  development  of  the  object"  remoininv  after the coap  fiaj been  cut  by  tap  plane  CD. 
The  devolopmf.nl"  of  this  remain/ny  object  is  here  shonn.  The  student"  should  observe  that  the  distance  4-/Oir> 
thf  top  view  equals  twice  the  distance  Mttin  the  front  view.  He  should  a/so  remember  Hiat  a/lofthf  distances  in 
the  development  from  O  to  the  curve  I9-I3-/9  ore  obtained  from  rhe line  O-20  in  the  front  vie*  and  should  not  be 
measured  on  any  other  e/empnt. 

Plate  35 -drawn  on  an  entirely  separate  sheet-  tal/s  fora  development  of  the  object /eft af/er the cone  has 
been  cut  by  the  fl/anp  A \-8.  Thf  dratviny  of  this  exercise  shout</ demonstrate  whether  or  not  the  studentbas 
mastered  the  principles  presented  by  plate34-.   The  method  of  procedure  is  the  same. 


vtews  a/  Me  cow 
S  ty  pfcne  JBfor  fitofe 


DEVELOPMENT  OF  A  CONE  CUT  BY  PLANE 
•.  Cut  ty  pbne  SCALE    FVUU 


P'A.TE' 


NO- 


Ki 
No. 


52 


THIS    CIRCLE  INTO    24- 

ANP    LAY    THEM    Off    ON    A'  STRAIGHT 
LINE     TO    PETERMINE      LCNSTM    OF      MN 


X 


(K»-reR3ECTIOM      Of    THREE     PIPES 


53 


INTERJECTION  Of  SQUARE 


SCALE.       FULl. 
PRAWN     BY 
PA.TE 


HEX.  PYRAMID 


-rt 
.     O   ( 


54 


THIS    CIRCLE     INTO    24-  EQUAL. 
LAY    THEM    OPT   ON    A.    STRAIGHT  LINE    TO 
PETEI?MIN&      LENGTH     OR 


INTERSECTION    OF  CYLINDER    AMP   SQUARE    PYRAMID 

-  SI7E. 

BV 
E- 

F=i-*>-rE    NO. 


55 


INSTRUCTIONS 

TRANSFER     THIS    DRAWING  TO  THE     REGULAR    SIZE    SMBET    UMNG 
THE     PIVIDEEJ    ANP   MAKING     THE    DRAWING    ON  THE    OTHER. 
SHEET     TWICE.     TME,     SIZE      SHOWN    HERE.-    DEVELOP  THE  OBJECT, 
COT     OUT     THE.      PEVELOPMBNTi     AND    PASTE.     THEM  TOGETHER 
TO     FOR.M     THE     OBJECT     ILLUSTRATED     IN    THE    VPPER,    RiCHT 

HAND     COK.NER..    W>E.    THIN    PA.PE.R.     ALLOV-    I_AP»    TOR. 


PEVCLOPMENT    PROBLEM 


BV 
PATE- 


NO 


56 


PLATE  40. 

Select  any  one  of  the  objects  sketched  on  the  following  page,  draw  its  development  full  size,  cut  it  out,  and 
paste  it  together.     Do  not  forget  to  allow  for  the  lap. 


57 


PEVELOPMENT 

SCALE     njL-U.    SIZE. 

PRAWN    BY 

PATE. 

PLATE     NO  . 


40 


58 


DETAIL  AND  ASSEMBLY  DRAWING. 

The  more  practical  work  of  the  course  begins  with  Plate  41.  All  work  must  be  laid  out  in  pencil  first,  and  the 
pencil  drawing  must  be  just  as  complete  as  the  finished  drawing  is  to  be.  Neat  work  is  exceedingly  important.  The 
appearance  of  the  plate  will  depend  much  upon  the  way  the  lettering  is  done.  Many  sketches  are  given,  but  this  does 
not  imply  that  students  are  to  make  a  sketch.  Follow  dimensions  and  make  a  finished  drawing.  Ink  or  trace  accord- 
ing to  directions.  Students  should  study  the  several  plates  very  carefully  before  proceeding  with  the  work. 

Pages  60  and  61  contain  sketches  of  the  objects  drawn  on  the  plates  designated.  These  sketches  should  be 
carefully  studied  before  and  while  drawing  the  object  in  orthographic  projection. 

Several  plates  require  that  a  sketch  be  made  of  an  object,  the  object  measured,  and  the  dimensions  obtained 
to  be  put  upon  the  sketch.  This  should  be  very  carefully  done,  a  particular  effort  being  made  to  get  all  of  the  neces- 
sary dimensions  on  the  sketch. 

All  assembly  drawings  must  represent  the  very  best  skill  of  the  student;  Great  care  should  be  taken  with 
the  drawing  of  the  different  kinds  of  lines.  No  assembly  drawing  is  to  contain  free-hand  lettering.  All  letters  must 
be  drawn  with  the  instruments. 

When  a  drawing  is  to  be  traced  stretch  the  tracing  cloth  over  the  drawing  and  ink  in  the  same  way  as  when 
a  pencil  drawing  is  inked.  The  dull  side  of  the  cloth  is  generally  used. 


61 


/fate  apenc//  drowny  and  ink  //• 


•SECTION    ON     A  B-C 


CRANK    PIN    WASHER 

•5CAUE      ITJL1-       SIZE 
DRAWN     BY 
PATE 

PLATE     NO.    ^ 


62 


/fade  a penal 'drawing  and  ink  it 


BOLSTER  CHAFING  PLATE 


40 

PLATE    N042 


63 


/m/ntef/ons 


. 

a  fxnc//  o/nzw/np  anS-rd:  fr 


CENTER 

5CALC1     6'- 1   FOOT 
PRAWN    BY 
PATE 

PLATE:  NO. 


64 


opend/dmwf/y 

skefcf)  and  ink  if-. 


3PRINS  LINK  5EAT 

<B~-  I  FOOT 


NO. 


65 


>y  o/Sfo 


i'K 
4  > 

•*  COOMTCR.SONV 

( 
i" 

4-4  — 

i        y 

M 

^rfe 

TLL 

C^^1     X 

Htfi 

"-A.". 


7'-4- 


17ETML  Or  CYLINDER  EQUALIZER" 

^"  -I  FOOT 
PRAV/N    BY 


NO. 


66 


//: 


c//  e/nwuy  of  M,s 


5<ALE  TO  BE 


ARM 


F^L-ATTE     NO 


67 


EXTENSION  HW171E  5HAKINQ 


a /**<://  c/mw/sy  o/ M/j  jfc/rt  one/ 


THE   «NUI»  TOR  TIC   RAW 
A.B.C    HMD  O  A<?t   AU  lAkTN 
ON    THE    CtNTCR    UNE    MN 


JOURNAL  PORTION  OF 
DCARING  BRACKET 

5CALE    FULL  5(2C 
DRAWN    BY 


/mfrucr/of?j .,  .  ..  , 

/fate  a  ff&x:// arawm? 
and  frace  if  ' 


PLATE     NO  46 


69 


SCREW  THREADS. 

It  is  frequently  desirable  in  machine  construction  to  fasten  certain  parts  together  in  such  a  way  that  they  can 
easily  be  put  together  and  taken  apart  again  without  injury  to  the  parts.  This  result  is  accomplished  by  using  fasten- 
ings having  screw  threads  cut  upon  them. 

There  are  many  different  kinds  of  threads,  the  ones  principally  used  being  shown  in  cross  section  on 
Plate  49. 

All  of  these  plates  are  to  be  first  drawn  in  pencil  and  afterwards  inked. 

The  student  is  advised  to  study  the  chapter  devoted  to  threads  from  some  good  book  on  Machine  Design. 
The  discussion  of  the  subject  is  of  such  length  that  it  is  impossible  to  give  space  to  it  in  this  particular  book. 


TABLE   OF  SIZES   OF  TAP   DRILLS. 


WROUGHT    IRON    PIPE  THREAD. 


Tap 

Diameter 
Inches 

Threads 
per  Inch 

Drill  for 
V  Thread 

Drill  for 
U.S. 

Standard 

Drill  for 

Whitworth 

1-4 

16,  18,  20 

5-32,     5-32,  11-64 

3-16 

3-16 

9-32 

16,  18,  20 

3-16,  13-64,  13-64 

5-16 

16,  18 

7-32,  15-64 

1-4 

15-64 

11-32 

16,  18 

1-4,     17-64 

3-8 

14,  16,  18 

1-4,       9-32,     9-32 

9-32 

9-32 

13-32 

14,  16,  18 

19-64,  21-64,  21-64 

7-16 

14,  16 

21-64,  11-32 

11-32 

11-32 

15-32 

14,  16 

23-64,     3-8 

1-2 

12,  13,  14 

3-8,     25-64,  25-64 

13-32 

3-8 

9-16 

12,  14 

7-16,  29-64 

7-16 

5-8 

10,  11,  12 

15-32,     1-2,       1-2 

1-2 

1-2 

11-16 

11,  12 

9-16,     9-16 

3-4 

10,  11,  12 

19-32,     5-8,       5-8 

5-8 

5-8 

13-16 

10 

21-32 

7-8 

9,  10 

45-64,  23-32 

23-32 

23-32 

15-16 

9 

49-64 

1 

8 

13-16 

27-32 

27-32 

Size 
of  Pipe 
Inches 

B 

c 

E 

D 

A 

Threads 
per 
Inch 

1-8 

.27 

.40 

.39 

.33 

.19 

27 

1-4 

.36 

.54 

.52 

.43 

.29 

18 

3-8 

.49 

.67 

.66 

.57 

.30 

18 

1-2 

.62 

.84 

.82 

.70 

.39 

14 

3-4 

.82 

1.05 

1.03 

.91 

.4 

14 

1 

1.05 

1.31 

1.28 

1.14 

.51 

11   1-2 

1   1-4 

1.38 

1.66 

1.63 

1.49 

.54 

11    1-2 

1   1-2 

1.61 

1.9 

1.87 

1.73 

.55 

11   1-2 

2 

2.07 

2  3-8 

2.34 

2.2 

.58 

11   1-2 

2  1-2 

2.47 

2  7-8 

2.82 

2.62 

.89 

8 

3 

3.07 

3  1-2 

3.44 

3.24 

.95 

8 

3  1-2 

3.55 

4 

3.94 

3.74 

1 

8 

Size  of  pipe  is  inside  diameter.     D=diameter  at  bottom  of  the  thread.     B= 
inside  diameter  of  pipe.     C=outside  diameter. 


71 


Xf?EW   THREAPS 

SCALJE    FTJLL    SIZE. 
PRAWN     BV 


NO. 


72 


INSTRUCTIONS   FOR   PLATE  50. 

Draw  the  top  and  front  views  of  three  cylinders  well  spaced  upon  the  sheet.  Divide  each  of  the  circum- 
ferences into  twelve  equal  parts.  This  is  easily  done  by  using  the  30-60  triangle. 

Figure  1  represents  the  drawing  of  the  curve  called  the  helix.  This  curve  is  generated  by  a  point  moving  in 
a  horizontal  direction  upon  the  surface  of  a  moving  cylinder.  The  point  of  a  threading  tool  in  a  lathe  will  generate 
a  helix  upon  the  moving  piece  of  metal  from  which  the  thread  is  to  be  made.  The  distance  from  A  to  B  represents 
the  pitch  of  the  thread,  and  this  must  be  divided  into  exactly  the  same  number  of  parts  as  contained  in  the  circum- 
ference. This  is  twelve  in  this  particular  case.  Project  down  from  the  points  on  the  circumference  intersecting  lines 
drawn  from  the  points  on  A  B.  By  connecting  the  intersections  the  points  of  the  helix  may  be  obtained. 

Figure  2  shows  how  the  curves  of  the  V  thread  are  obtained.  The  pitch  in  this  instance  is  \" .  This  is  divided 
into  twelve  equal  parts  just  as  A  B  was  in  Figure  1.  The  intersections  are  obtained  in  the  same  way.  Note  that  the 
inner  circumference  C  represents  the  diameter  at  the  bottom  of  the  thread,  and  that  the  curve  of  the  bottom  of  the 
thread  is  obtained  by  projecting  down  from  the  points  where  the  diameters  cut  this  circumference. 

Figure  3  gives  the  curves  of  the  square  thread.  Apply  the  principles  used  in  the  preceding  figures  to  obtain 
the  curves.  The  pitch  of  the  thread  in  this  case  is  one  inch. 


73 


FISORE 


THE    HELIX  AMP   1T5    APPLICATION 
SCALE     FULL 

PFSAWN    BY 


PLATE     NO 


74 


MOPIFIEP    SQUARE    OR    ACME    THREAP 


I 


PER;  INCH 


V  THREAD 


'CONVENTIONAL     THREADS 


z  .. 

Setr/ons  os  0/7  f/ofp  49    oad  connect"  fofart?   obfarnecf  /n  orcfcr 

-  \/Sf*VJ    OJ  shewn     o&trvf. 


PATE 


NO 


75 


A- THICKNESS    OF   NUT  =  P=  PlA.   OF    BOLT 


t5  =  THKKNE5S    or  HEAP  OF  BOLT  =      ^_ 
C  15   03TAINEC?    BY   CONSTRUCTING    HEAA<SON 
EL=»  DISTANCE.    BETWEEN    PARALLEL  S1PES  OF  HEXAGON  -  ^  +^' 

5TANPAI?P  HEXAGONAL  BOLT  AtlP  NUT 

SCAU&     FVI_1_   SIZE. 
C?RAV/|vJ      BY 

MO. 


76 


PLATE  53. 

Details  of  the  several  parts  of  a  globe  valve  are  here  shown.  A  finished  drawing  from  these  details  is 
to  be  made  and  the  penciled  drawing  traced.  The  location  of  the  parts  upon  the  sheet  should  be  determined  upon 
before  starting.  Use  considerable  care  in  dimensioning.  Do  not  trace  the  drawing  until  the  assembly  is  completed. 
Every  detail  drawing  should  have  lettered  on  it  the  material  of  which  the  piece  is  made,  the  surfaces  to  be  finished 
(machined)  denoted  by  "f,"  and  the  number  of  each  part  wanted  to  make  a  complete  whole. 


PLATE  54. 

As  soon  as  the  penciled  detail  drawing  of  the  globe  valve  is  completed,  from  these  details  make  an  assembly 
drawing  as  shown.  Half  is  in  section,  half  shows  an  outside  view.  This  should  be  executed  on  a  good  grade  of 
white  paper  ("Whatman's,"  for  example),  and  every  effort  should  be  made  to  produce  a  particularly  well  finished 
drawing.  There  should  be  no  free-hand  work  at  all,  not  even  the  lettering.  The  reason  why  it  is  advisable  to  make 
the  assembly  from  the  pencil  drawing  of  the  details  is  that  a  check  on  the  accuracy  of  the  several  details  can  thus  be 
obtained.  The  parts  will  not  fit  together  to  make  the  whole  if  they  are  not  correct.  The  size  of  the  sheet  is  14i"x 
20^"  outside  dimensions,  one-inch  border. 


PETA1D  OF  SLOPE  VALVE 

XALE     O'- 1 TT  ANP  fULL  y2f. 
PRAWN    BY 


78 


79 


PLATE  55. 

For  this  Plate  the  student  will  be  given  a  casting  of  some  kind  or  any  detail  of  a  machine  of  a  fairly  compli- 
cated nature  and  be  required  to  make  a  proper  sketch  of  the  same  fully  dimensioned.  The  dimensions  will  have 
to  be  obtained  by  actual  measurement.  The  sketch  should  be  very  carefully  made,  and  an  extreme  effort  should  be 
made  to  get  all  dimensions,  properly  arranged,  thereon.  From  this  sketch  a  pencil  drawing  is  to  be  made  which  in 
turn  is  to  be  traced. 

Obviously  the  final  drawing  cannot  be  made  unless  the  sketch  is  complete  in  every  detail. 


80 


PLATE  56. 

A  more  complicated  object  should  be  selected  for  this  drawing  than  that  covered  by  Plate  55.  The  injector, 
as  represented  by  the  assembly  drawing  on  Page  82,  makes  an  excellent  thing  because  of  the  number  and  shape  of 
the  details.  Measurements  must  first  be  taken  and  sketches  made.  These  sketches  must  be  complete,  especially 
as  far  as  dimensions  are  concerned.  The  pencil  detail  drawing  is  to  be  made  from  the  sketches.  There  is  to  be 
but  one  sheet  of  details,  and  the  proper  scales  must  be  selected  so  that  this  can  be  done.  The  injector  here  given 
is  a  "  Lukenheimer." 


PLATE  57. 

Make  an  assembly  drawing  of  the  object  selected.    Half  to  be  shown  in  section,  half  an  outside  view.    No 
free-hand  lettering  on  this  plate.    Size  of  plate  to  be  14£"x2(H"  outside  dimensions  with  a  one-inch  border. 


si 


I. 


i  *  I  & 


^  fe  K 


:  I 

-I  K 

2  ° 

to 


PLATE  58. 

Sketch  a  lathe,  a  motor,  a  steam  engine,  or  some  similar  object,  and  draw  the  front  and  side  views  of  it. 
This  must  be  very  well  done.  No  free-hand  lettering  is  allowed.  The  sheet  is  to  be  20!"  x  29"  outside  dimen- 
sions, with  a  1  \"  border.  An  idea  of  what  is  wanted  can  be  obtained  from  the  following  drawing  on  Page  84.  Draw 
this  on  white  paper  ("Whatman's"  is  suggested)  and  ink  it. 


83 


SCALE       THREE      INCHES  •  DNE       FDm 
DR*WN       BY       E     Q     PATCH. 
NDV.    H-ilRl^h 

PUATE:    ND.  SB. 


84 


TABLE  OF  DECIMAL  EQUIVALENTS 


of 


8ths,  16ths,  32ds,  and  64ths  of  an  inch 


8ths 

11-16   =   .6875 

19-32   =   .59375 

9-64    =   .140625 

37-64   =   .578125 

1-8     =   .125 

13-16   =   .8125 

21-32   =   .65625 

11-64   =   .171875 

39-64   =   .609375 

1-4     =   .250 

15-16   =   .9375 

23-32    =   .71875 

13-64   =   .203125 

41-64   =   .640625 

3-8     =   .375 

25-32   =   .78125 

15-64   =   .234375 

43-64   =   .671875 

1-2     =   .500 

32ds 

27-32   =   .84375 

17-64   =   .265625 

45-64   =   .703125 

5-8     =   .625 

29-32   =   .90625 

19-64   =   .296875 

47-64   =   .734375 

1-32   =   .03125 

3-4     =   .750 

31-32    =   .96875 

21-64   =   .328125 

49-64   =   .765625 

3-32   =   .09375 

7-8     =   .875 

5-32   =   .15625 

23-64   =   .359375 

51-64   =   .796875 

16ths 

7-32   =   .21875 

25-64   =   .390625 

53-64   =   .828125 

1-16  =   .0625 

9-32   =   .28125 

64ths 

27-64   =   .421875 

55-64   =   .859375 

3-16  =   .1875 

11-32   =   .34375 

1-64   =   .015625 

29-64   =   .453125 

57-64   =   .890625 

5-16  =   .3125 

13-32   =   .40625 

3-64   =   .046875 

31-64   =   .484375 

59-64   =   .921875 

7-16  =   .4375 

15-32   =   .46875 

5-64   =   .078125 

33-64   =   .515625 

61-64   =  .953125 

9-16  =   .5625 

17-32   =   .53125 

7-64   =   .109375 

35-64   =   .546875 

63-64   =   .984375 

85 


f 

may   o£>fo/f?  art  /'c/?a    of 

a/-  We  soix?  ///??<?  JasnJ//or7ze 


Mot 


from  cfea'/na/  fa  f/&cf/o/7a/  form 
are 


. 
/s  -fa  fre  draw/?  sr>  penc//  ontf  / 


HOOK.. 

FULL.    SI'Z 
BT 


86 


PLATE  60.     THE   CYCLOID. 

If  a  mark  was  made  upon  the  circumference  of  a  circle  at  the  exact  point  of  contact  with  a  plane,  the  mark, 
as  the  circle  revolved  along  the  plane,  would  follow  a  curve  called  the  cycloid. 

To  generate  this  curve,  draw  any  circle,  as  D  E  F,  and  divide  its  circumference  into  any  number  of  equal  parts 
(in  this  case  use  twelve).  Draw  a  straight  line  tangent  to  the  circle  at  F,  and  on  it  lay  off  six  divisions,  each  equal 
to  a  division  of  the  circle.  From  a,  b,  c,  d,  e,  and  f  draw  perpendiculars  cutting  the  center  line  of  the  circle.  Taking 
these  points  as  centers,  swing  arcs.  On  these  arcs  lay  a-6  equals  one  division  of  the  circle;  b-7  equals  two  divisions; 
and  so  on  until  point  11  is  obtained.  Connect  the  points  to  obtain  the  curve.  Draw  the  circle  DEF  two  inches  in 
diameter. 

THE  ARCHIMEDEAN   SPIRAL 
The  spiral  is  a  curve  which  makes  one  or  more  revolutions  round  a  fixed  point,  but  does  not  return  to  itself. 

To  construct  the  Archimedean  Spiral,  draw  any  circle  and  divide  it  into  any  number  of  equal  parts.  Divide 
the  radius  into  the  same  number  of  equal  parts,  and  draw  concentric  circles  through  these  points  of  division.  The 
intersections  of  these  circles  with  the  diameters  will  give  the  points  of  the  spiral.  Connect  1,  a,  b,  c,  d,  e,  f,  g,  h,  k, 
m,  and  n  to  obtain  the  curve.  Take  1-7  in  this  case  as  five  inches. 

THE   INVOLUTE. 

If  a  perfectly  flexible  line  was  wound  round  any  curve  and  kept  stretched  as  it  was  gradually  unwound,  any 
point  in  the  line  would  trace  another  curve  called  the  involute  of  the  curve. 

Draw  any  circle  (in  this  instance  two  inches  in  diameter)  and  divide  it  into  any  number  of  equal  parts.  Draw 
tangents  to  the  circle  at  each  point  of  division,  a-2  equals  one  division  of  the  circle;  b-3  equals  two  divisions,  and  so 
on.  Connect  the  points  obtained  for  the  desired  curve. 

87 


THE      ARCHlplEPEAN   SPIRAL 


THE    cvcLotc? 


THE.    INVOLUTE.. 


5CALE     PULL. 


CONSTRUCTION 


/^  r^ 

.  6O 


PLATE  61.     THE   EPICYCLOID. 

When  a  circle  rolls  round  the  edge  of  another  circle  instead  of  along  a  straight  line  the  curve  called  the  epicy- 
cloid is  generated. 

Draw  the  pitch  circle,  taking  any  convenient  radius.  (Take  4?"  here.)  Draw  the  generating  circles  of  any 
diameter  less  than  the  radius  of  the  pitch  circle.  Divide  one  of  the  generating  circles  into  any  number  of  equal 
parts,  and  starting  at  A  lay  off  these  divisions  on  the  pitch  circle.  In  this  case  take  six  on  each  side  of  A.  Draw 
radial  lines  through  these  points  of  division  and  obtain  a,  b,  c,  d,  e,  and  f.  Taking  a,  b,  c,  d,  e,  and  f,  and  also  g,  h,  i, 
j,  k,  and  I  as  centers,  swing  arcs  using  the  radius  of  the  generating  circle.  Take  6-n  and  6-t  equal  to  one  division  of 
the  generating  circle;  7-u  and  7-o  equal  two  divisions;  and  so  on  until  the  curve  is  complete.  At  the  left  construct 
another  curve  similar  to  the  one  given. 

If  the  generating  circle  rolls  inside  of  instead  of  outside  of  the  pitch  circle,  the  curve  obtained  is  called 
the  Hypocycloid. 


89 


GENERATING    CIRCLET- 


THE     EPICYCLOIP 


GEOMETRICAL     CONSTRUCTION 


SCALE.     FVL.U     SJ-Z 
PRAWN     BY 


TMO. 


.       Ol 


90 


PLATE  62. 

Figure  1  is  a  representation  of  a  "heart"  cam.  This  type  of  cam  is  used  when  a  movement  both  up  and  down 
is  desired  gradual  and  constant. 

Draw  the  friction  roller  C  in  any  convenient  position.  Draw  the  5h"  circle  and  assume  that  B  is  the  maximum 
position  of  the  center  of  the  roller.  Divide  the  distance  from  B  to  C  into  eight  equal  parts,  and  divide  the  5\"  circle 
into  twice  this  number.  Draw  the  radial  lines  through  the  points  of  division  on  the  circumference.  Set  the  com- 
passes to  the  radius  of  the  roller,  and  taking  the  intersections  of  the  radial  lines  and  the  circles  as  centers,  draw  the 
dotted  circles.  Starting  at  A,  draw  the  outline  of  the  cam  tangent  to  the  circles.  The  right  half  of  the  cam  is  here 
drawn.  The  student  is  expected  to  complete  the  whole  cam.  This  is  to  be  inked. 

Figure  2  shows  a  cam  designed  to  produce  a  compound  motion.  Draw  a  circle  of  5i"  diameter,  assume  the 
lower  position  of  the  center  of  the  roller  to  be  at  A,  and  divide  the  distance  from  A  to  B  into  six  equal  parts.  The 
entire  circumference  is  to  be  divided  into  twelve  equal  parts.  Set  the  compasses  to  the  radius  of  the  roller,  and 
draw  the  dotted  circles  as  shown.  Starting  at  C,  draw  the  outline  of  the  cam  tangent  to  the  dotted  circles  until  the 
270°  line  is  reached.  Divide  the  circumference  from  270°  to  330°  into  twelve  equal  parts,  and  draw  radial  lines  through 
these  points  of  division.  Also  divide  EF  into  12  equal  parts  and  draw  arcs  through  the  points.  The  intersections 
of  the  arcs  and  the  radial  lines  will  give  the  points  necessary  for  a  gradual  return  from  G  to  the  starting  point.  In 
this  particular  cam  the  motion  rises  two  spaces  in  60°,  rests  for  30°,  rises  two  more  spaces  in  60°,  rests  for  30°,  rises 
two  more  spaces  in  60°,  rests  for  30°,  gradually  returns  towards  original  position  in  60°,  and  rests  for  30°  before  actually 
reaching  there.  This  drawing  is  to  be  inked. 


91 


•io 


CAM    PE5KSM 

FVL.U    SI/TE. 

BY 
PATE. 

PL-ATI 


NO 


62. 


92 


SYMBOLS 


GEARING   FORMULXE. 


TO   FIND 


FORMUUE 


Diametral  Pitch     .     .     . 

.     -     P 

Diametral  Pitch     .... 

p 

3.1416 

P' 

Circular  Pitch  .... 

.     -     P' 

Circular  Pitch 

P' 

3.1416 

P 

Pitch  Diameter      .     .     . 

.     -     D 

Pitch  Diameter 

D 

N 

P 

Center  Distance     .     .     . 

.     -     C 

Center  Distance 

c 

N+N, 

2P 

Addendum  .     .     .     .     ; 

.     -     S 

Addendum 

Q 

P' 

3.1416 

Dedendum  

.     -     d 

Dedendum 

d 

0 

Clearance     

.     -     F 

Clearance 

F 

0.157 

P 

Thickness  of  Tooth     .     . 

.     -     T 

Thickness  of  Tooth      .     .     . 

.      .      .      .     T 

.48P' 

Space  between  Teeth 

.     -     W 

Space  between  Teeth  . 

.      .      .      .     W 

=      .52P' 

Outside  Diameter  .     .     . 

.     -     O 

Outside  Diameter 

o 

N+2 

P 

Number  of  Teeth  .     .     . 

.     -     N 

Number  of  Teeth   .... 

.      .      .      .     N 

=     PxD 

Length  of  Rack     .     .     . 

-     L 

Lenath  of  Rack 

L 

NP' 

93 


TEMPLET   FOR   GEAR  TEETH. 

When  it  is  necessary  to  show  the  teeth  in  a  complete  gear  wheel,  it  would  require  much  time  and  labor  to 
draw  each  tooth  separately.  This  labor  is  saved  by  constructing  an  accurate  pattern  or  templet  of  the  proper  tooth 
outline  and  tracing  the  outlines  of  the  whole  number  of  teeth  in  the  gear  from  the  pattern. 

In  constructing  the  templet,  proceed  as  though  drawing  one  tooth  of  the  gear.  The  pitch,  addendum,  deden- 
dum,  and  clearance  circles  are  drawn,  and  the  complete  curve  of  one  half  the  tooth  laid  out.  Only  one  side  of  the 
tooth  outline  need  be  drawn,  as  in  tracing  around  the  templet  in  the  finished  drawing  half  the  teeth  are  drawn  first 
and  the  other  half  formed  by  turning  the  templet  over  with  the  reverse  side  uppermost.  This  makes  the  two  sides 
of  the  teeth  similar. 

The  templet  is  cut  out  in  the  form  shown  in  the  cuts  illustrating  the  involute  and  cycloidal  templets  on  the 
following  pages.  The  divisions  marking  the  tooth  widths  and  spaces  are  laid  off  on  the  pitch  circle  of  the  finished 
drawing,  and  the  templet  pinned  on  with  the  center  point  at  its  lower  end  directly  over  the  center  of  the  pitch  circle 
of  the  drawing.  Then  by  revolving  the  templet  the  right  sides  of  all  the  teeth  are  traced  at  the  points  already  deter- 
mined on  the  pitch  circle.  By  reversing  the  templet  the  teeth  are  completed  as  described  above. 

The  templet  should,  if  possible,  be  cut  from  medium  weight  cardboard,  as  the  clean-cut  edge  of  the  tooth 
outline  will  retain  its  proper  shape  longer  when  a  large  number  of  teeth  are  to  be  drawn.  Sometimes  the  draftsman 
is  called  upon  to  draw  gears  of  a  certain  definite  size  which  have  become  standard  in  certain  lines  of  work.  The  temp- 
lets may  then  be  constructed  of  some  durable  substance,  such  as  hard  rubber  or  celluloid,  and  filed  away  for  future 
use. 


94 


TEMPLET   FOR    INVOLUTE  TEETH.     FIGURE   1. 

(1)  Draw  the  pitch,  addendum,  dedendum,  and  clearance  circles.  (2)  Draw  the  perpendicular  radius  oa 
prolonged,  intersecting  the  pitch  circle  at  b.  (3)  Draw  the  line  of  obliquity  x  y  through  point  b  at  an  angle 
of  15°  with  the  horizontal  line  b  z.  (4)  With  o  as  a  center  draw  the  base  circle  tangent  to  the  line  x  y  at  the  point 
c. '  (5)  From  c  lay  off  to  the  left  on  the  base  circle  the  divisions  c-1,  c-2,  c-3,  etc.,  and  to  the  right  the  divisions  c-6, 
c-7,  etc.  These  divisions  should  each  be  less  than  one  tenth  the  diameter  of  the  base  circle.  (6)  At  the  points  1, 
2,  3,  4,  etc.,  draw  the  tangents  to  the  base  circle  T,-1,  T2-2,  T3-3,  etc.  (7)  Using  the  radius  c  b  with  point  c  as  cen- 
ter, draw  the  tooth  curve  as  far  as  the  first  tangent  T,  from  b,  thus  giving  point  d  on  tangent  Ti.  (8)  Taking  the 
next  radius  cd,  the  curve  is  continued  to  the  next  tangent  T2,  giving  point  e.  (9)  By  successively  using  the  remain- 
ing radii,  ce,  cf,  etc.,  the  curve  is  carried  a  little  beyond  the  outside  or  addendum  circle.  (10)  The  lower  part  of 
the  tooth  curve  between  the  pitch  and  base  circles  is  obtained  by  using  the  radii  c  b,  c  k,  and  en.  (11)  The  tooth 
edge  below  the  base  circle  is  radial  to  center  o,  and  the  fillet  joining  the  side  of  the  tooth  to  the  whole  depth  or  clear- 
ance circle  is  drawn  with  a  radius  equal  to  one  seventh  the  distance  between  two  adjacent  teeth  taken  on  the  adden- 
dum circle. 

INVOLUTE   RACK  WITH   STRAIGHT   FLANKED  TEETH.     FIGURE  2. 

(1)  Draw  the  addendum,  pitch,  dedendum,  and  clearance  lines.  (2)  From  a  lay  off  the  linear  pitch  a  b  which 
corresponds  to  the  circular  pitch  in  circular  gears.  (3)  Then  after  locating  point  c,  which  gives  the  tooth  width,  draw 
all  left-hand  sides  of  the  teeth,  such  as  d  e,  through  the  pitch  points  at  an  angle  of  75°  with  the  pitch  line.  (4)  The 
right-hand  edges  of  the  teeth  are  also  drawn  at  75°  from  the  pitch  line,  but  in  the  opposite  direction  of  obliquity.  (5) 
The  fillets  at  the  bottom  of  the  space  are  drawn  with  a  radius  equal  to  one  seventh  of  the  distance  between  two  adja- 
cent teeth  measured  on  the  addendum  line. 


TEMPLET  FOR   CYCLOIDAL  TEETH.     FIGURE  3. 

(1)  Draw  all  gear  circles  as  in  the  drawing  of  the  involute  templet.  (2)  Draw  radius  o  a  intersecting  pitch 
circle  at  point  b.  (3)  From  b  lay  off  on  the  pitch  circle  the  divisions  b-1,  b-2,  b-3,  etc.,  to  the  right,  and  b-7,  b-8, 
b-9,  etc.,  to  the  left.  (4)  From  points  1,  2,  3,  4,  etc.,  draw  the  internally  radial  lines  to  the  pitch  circle,  and  from 
points  7,  8,  9,  etc.,  draw  the  externally  radial  lines  to  the  pitch  circle.  (5)  With  a  radius  less  than  one  half  the 
radius  of  the  pitch  circle,  and  with  r,  as  a  center,  draw  the  first  internal  generating  circle  pc  tangent  to  the  pitch 
circle  at  point  1.  (6)  With  the  same  radius,  and  with  the  points  r2,  r3,  r4,  etc.,  as  centers,  draw  the  other  internal 
generating  circles.  (7)  The  external  generating  circles  are  drawn  with  the  same  radius  from  points  r7,  r8,  etc.  (8) 
Set  the  dividers  at  the  distance  b-1  on  the  pitch  circle,  and  from  point  1  lay  off  this  distance  b-1  on  the  first  generat- 
ing circle  p  c.  (9)  On  the  next  generating  circle  lay  off  two  divisions,  each  equal  to  b-1,  from  point  2.  (10)  On 
the  next  generating  circle  lay  off  three  divisions,  each  equal  to  b-1,  from  point  3.  (11)  Continue  to  lay  off  these 
divisions  on  the  generating  circles  until  they  pass  below  the  clearance  circle.  (12)  The  points  d,  e,  f,  g,  give  the 
direction  of  the  tooth  curve  between  the  pitch  and  clearance  circles.  (13)  Using  the  same  length,  b-1,  step  off  one 
division  from  point  7  on  the  first  external  generating  circle.  (14)  By  laying  off  two  divisions  from  point  8  and  three 
divisions  from  point  9  we  get  the  points  h,  k,  m,  and  n,  which  give  the  direction  of  the  upper  part  of  the  tooth  curve. 
(15)  Connecting  points  n,  m,  k,  h,  b,  d,  e,  f,  and  g,  the  whole  curve  of  the  tooth  is  obtained.  (16)  The  fillet  at  the 
bottom  of  the  curve  is  drawn  with  a  radius  equal  to  one  seventh  the  distance  between  two  adjacent  teeth  measured 
on  the  addendum  circle. 


£       APPENPUM 


^} 

OUUIPE    ClRUE 

H  CIRCLE: 


CLEARANCE. 


TLfMPLET 


97 


PLATE  63. 
Draw  a  spur  gear  of  22  teeth,  3"  circular  pitch.     Use  the  involute  method. 

PLATE  64. 
Draw  a  spur  gear  of  24  teeth,  1     diametral  pitch.     Use  the  cycloidal  method. 

PLATE  65. 
Draw  a  rack  and  pinion  of  18  teeth,  2"  circular  pitch.     Use  either  method. 

(The  complete  gear  in  the  above   problems  cannot  be  constructed  to  full  scale.     If  full  scale  is  used,  draw 
as  much  of  the  gear  as  possible.    These  drawings  should  be  inked.) 


98 


BEVEL  GEARS. 

The  method  of  laying  out  bevel  gear  blanks  is  shown  in  Figure  4.  (1)  Draw  the  center  lines  of  gear  shafts 
A  B  and  C  D  90°  apart  and  intersecting  at  point  0.  (2)  From  O  measure  down  on  line  C  D  a  distance  of  one  half 
the  pitch  diameter  of  gear  Y  and  draw  the  pitch  line  E  F  of  gear  X  parallel  to  the  line  A  B.  (3)  From  O  measure  to 
the  left  on  line  A  B  a  distance  of  one  half  the  pitch  diameter  of  gear  X  and  draw  pitch  line  G  H  of  gear  Y  parallel 
to  line  C  D.  The  two  pitch  lines  will  intersect  at  point  J.  (4)  From  K  on  line  A  B  measure  off  the  distance  J  K 
on  line  G  H  locating  point  M.  This  gives  the  pitch  diameter  J  M  of  gear  Y.  (5)  From  L  on  line  EF  measure  off 
the  distance  J  L  locating  point  N.  This  gives  the  pitch  diameter  J  N  of  gear  X.  (6)  Draw  the  front  cone  pitch  lines 
0  M,  O  J,  and  O  N.  (7)  Through  M  and  perpendicular  to  0  M  draw  the  back  cone  line  M  P,  and  from  point  P 
perpendicular  to  0  J  draw  the  back  cone  lines  JP  and  J  Q.  By  drawing  a  line  from  0  through  point  N  the  last 
back  cone  line  Q  N  is  obtained.  (8)  From  M  lay  off  the  addendum  distance  M-1,  the  dedendum  distance  M-2, 
and  the  clearance  2-3.  (9)  These  distances  are  also  laid  off  from  points  J  and  N,  giving  points  4,  5,  6,  7,  8, 
9,  and  10.  (10)  Draw  the  lines  0-1,  O-2,  O-3,  O-4,  0-5,  0-6,  O-7,  O-8,  O-9,  and  O-10.  (11)  The  length  of 
the  tooth  face  1-12  is  made  about  one  third  the  length  of  the  front  cone  line  0-1.  (12)  The  proportions  of  such 
details  as  the  thickness  of  metal  in  the  gears,  the  length  of  the  hubs,  and  the  diameters  of  the  shaft  bores,  are 
left  to  the  student  to  design.  The  cross-sectioned  portions  show  where  the  metal  would  be  cut  if  a  plane  were  passed 
through  the  two  gears. 


2-4-  aitf  26  fee?/?  - 
/- 
as 


H 


\       I 

•  o  /yo/f-  oj  £cve/ aeerj   of    \ 
-!—•' ~-<-  ?sho/te  of    \ 


5EVEL    GEAR. 

SCALE    To   em.    PETCRMINEP' 


PATE 

PLATE     MO. 


100 


ISOMETRIC   PROJECTION. 

Isometric  projection  is  a  method  of  drawing  by  means  of  which  a  pictorial  effect  can  be  obtained  without 
destroying  the  relative  proportions  of  the  several  parts  of  the  object.  Measurements  taken  on  the  vertical  or  thirty 
degree  lines  of  an  isometric  drawing  are  in  their  true  length.  No  dimensions  should  be  taken  on  any  other  lines 
than  these. 

When  drawing  the  plates  numbered  67,  68,  69,  and  70,  draw  the  top  and  front  views  as  given  and  dimension 
them.  Place  no  dimensions  or  letters  on  the  isometric.  These  are  given  here  merely  to  show  the  connection 
between  the  two  types  of  projection  (Orthographic  and  Isometric). 

All  isometric  drawings  are  to  be  inked. 


101 


ra*    a  3"  cv&e  as.jfawn  //?  fi#  /.    /Safe  fovs   /6 
'     /wes  /»  Me  /v/j/afe  /?a;s?fi  a/  /fie  s/tfes  Jfv/n  Mf  efio 
ce/?ferj  .  fj  ///j  fn?r  /?ef&sory   /o  obfan  <y  surface  sue/?  as 
w  f   on  //><?  dtTfer.  as  '-  ~ 


c  v/evs  o/  e>  c/rc/e  /J  o6/-o//?f<s 
cor/rer?  and  f&t/n<?  f/?e  //?fes-jecf/orrj 
^farpdrva  eut  J/0/7?  ana/far  jt/rf?ce, 
3o~ffv/??  eac/?  corner  ^?/f>^/y  f/?e  sah/ 


/TO 


ISOMETRIC    PROJECTION 
SCALE:   FULL  SIZE- 
PRAWN    BY 

PATE.  f  «-7 

l     NO-    QD  / 


102 


cv 


o 

VI 

(0 


I5OMETRIC    PROJECTION 
SCALE  V»1  FOOT 


PATE. 


NO 


/  Q 
.     DO 


103 


IJL- 

12- 


7 


ISOMETRIC  PROJECTION 

SCALE    FULL  SI^E 
PRAWN    BY 

PATE.  , 

PLATE.    NO.  » 


104 


I50METRIC   PROJECTION 

SCALE     FULL  SIZE. 


NO. 


CVsTE. 


105 


PLATE  71. 

For  this,  the  final  isometric  drawing,  lay  out  a  sheet  whose  outside  dimensions  are  2(H"x29"  with  a  border 
of  H".  On  this  sheet  make  an  isometric  drawing  of  some  fairly  complicated  machine.  The  one  made  on  Plate  58 
is  suggested.  The  measurements  may  be  taken  directly  from  this  with  the  dividers  and  transferred  to  the  isometric. 
Make  all  letters  with  the  instruments.  Make  the  drawing  on  white  paper  ("Whatman's"  is  suggested)  and  ink  it. 


106 


PERSPECTIVE   DRAWING. 

If  one  were  to  look  out  of  the  window  at  a  building,  and  if  a  line  could  be  drawn  from  every  point  of  the  build- 
ing to  the  eye  of  the  observer,  the  points  on  the  window  where  the  lines  pierced  it  would  be  the  ones  to  be  con- 
nected if  a  picture  of  the  building  was  to  be  drawn  upon  the  window.    The  window  corresponds  to  the  picture  plane 
in  perspective  drawing  —  the  plane  upon  which  the  observer  and  object  rest  is  the  horizontal  plane  called  the  ground 
-the  plane  parallel  to  the  ground  and  passing  through  the  eye  of  the  observer  is  the  plane  of  horizon. 

Study  Plate  72  very  carefully  and  note  the  following:  A  B  is  a  top  view  of  the  picture  plane  —  C  D  is  a  front 
view  of  the  plane  of  horizon  —  E  F  is  a  front  view  of  the  ground  plane.  The  station  point  (the  point  at  which  the 
observer  stands)  is  usually  taken  at  about  one  and  one  half  the  height  of  the  object  in  front  of  the  picture  plane. 
This  point  must  be  selected  to  show  the  object  to  the  best  advantage.  The  line  of  horizon  is  generally  taken  from 
five  to  six  feet  above  the  ground.  Note  that  the  vanishing  points  are  obtained  by  drawing  lines  from  the  station 
point  parallel  to  the  faces  in  the  top  view  until  they  intersect  the  picture  plane,  and  then  dropping  perpendiculars 
to  the  line  of  horizon.  Note  how  lines  are  drawn  from  each  point  of  the  object  in  the  top  view  to  the  station  point 
and  perpendiculars,  then  dropped  from  the  intersections  of  these  lines  with  the  picture  plane. 

• 

Obviously,  in  reality,  the  object  would  never  be  against  the  picture  plane.  Plates  72  and  73  show  it  in  this 
position,  but  this  is  done  so  that  the  student  will  master  the  principles  of  perspective  easier.  The  remaining  plates 
are  to  be  drawn  with  the  object  away  from  the  picture  plane. 

All  of  the  perspective  drawings  are  to  be  inked  and  shaded.  If  all  dotted  and  construction  lines  are  drawn 
in  red  ink  the  general  appearance  of  the  drawing  will  be  greatly  improved. 


107 


TOP  VIEW   OF  Pit  i  UKE    PLANE 


\  r 


V 


f—  STATION    POINT 


V»-N|SHIN<3    POINT 

LINE    OF   HORI'ZON'T? 


p         SCAUE-    -a"=lF-OOT 
PATTE. 


MO. 


70 

.     (A- 


108 


manner  tof  for  ffa  p/vceay'np  as??. 

a 


/o  ffa  pic.  fare  jcxtyn?  /h 
f*  w/ 


PERSPECTIVE    t7f?AWING 

5CALE  4^'  =  <  FOOT 

BY 
PATE. 

PLATE.      NO. 


109 


PERSPECTIVE: 

SCAUE.  3;"  =   I  FOOT 
PRAWN    BY 
PACTE: 


110 


Show?    <y//f>o//r/3  /n 

ant/ 
curve  are 


/s  co//ec/  Xb  /V/t°  facf  //?<af  ffre 
//?  //<vf  some  manner-  as  of  far  /?a//rfr. 
A?f/-  as  0/7  excrc/se  Jar 


dravs/ha  of 


V 

L 

< 

- 

1  —  S                      — 

i 

t 

c 

\             L 

•-—  . 

/ 

, 

\ 

^^ 

«  4'o"  > 

«.           )o'-o"          v 

4.      AJ-(\      •*• 

\ 

/ 

IR'-O'  

\ 

JW5PKTIVE  DRAWING 

PRAWN    BY 


PLATTE    NO. 


111 


Mvdom  fre  asjtrft  ^  at-* 

-  #'  forotrr  /fate  aknv//itp  or? /a/ye 
g/ver?  fore  ~7/3/tt/er  (/vfartce}  e/vfff /fe  ofr/Kfe/y 
/fie  peapec//w  fehvce/?  Me  '//&??  and  xcfe  vtews    Draw 


PERSPECTIVE 

PRAWN    BY 
PATE 

PLA.TC     NO.     "7<5 


112 


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